禁忌学习神经元模型的电路设计及其动力学研究

对禁忌学习混沌神经元模型进行了详细的电路设计,包括单神经元、具有线性相似函数的双神经元以及具有二次相似函数的双神经元模型,并运用EWB(Electronic Workbench)电路仿真软件对所设计的电路进行了仿真,研究了电路中的Hopf分叉和混沌等非线性动力学现象,通过与数值仿真结果的比对验证了所设计电路的正确性与合理性. 关键词： 禁忌学习 神经元 电路设计 动力学     

五阶压控忆阻蔡氏混沌电路的双稳定性

通过在蔡氏电路的耦合电阻支路中串联一个电感,采用压控忆阻替换蔡氏电路中的蔡氏二极管,提出了一种新颖的五阶压控忆阻蔡氏混沌电路.建立该电路的数学模型,从理论上分析了平衡点及其稳定性的演化过程.特别地,该电路在给定参数下只有一个不稳定的零平衡点,却形成了混沌与周期的非对称吸引子共存的吸引盆,意味着双稳定性的存在.进而利用数值仿真与PSIM电路仿真着重研究了本文电路在不同初始状态下产生的双稳定性现象及其形成机理.PSIM电路仿真结果与数值仿真结果一致,较好地验证了理论分析.借助分岔图、李雅普诺夫指数、相轨图和吸引盆进一步深入探讨了归一化五阶压控忆阻蔡氏系统依赖于系统初始条件的动力学行为.结果表明,该忆阻蔡氏系统在不同的初始条件下能够呈现出混沌吸引子与周期极限环共存的双稳定性现象.     

单模激光混沌特性的理论研究

在光学中，激光是产生双稳态、振荡、混沌等多种自组织现象的典型例子。本文采用非线性理论分析了单模激光的混沌特性，对描述单模激光的非线性动力学方程进行了稳定性分析，从而确定了系统失稳后进入混沌态的分歧点，并利用计算机进行了数值计算，给出了系统呈现混沌态的模拟结果。计算机数值模拟的结果与理论分析的结果相吻合。     

基于忆阻器的多涡卷混沌系统及其脉冲同步控制

忆阻器是一种具有记忆功能和纳米级尺寸的非线性元件,作为混沌系统的非线性部分,能够提高混沌系统的信号随机性和复杂度.本文基于增广Lü系统设计了一个三维忆阻混沌系统.仅仅通过改变系统的一个参数,该系统能产生单涡巻、双涡卷和四涡巻的混沌吸引子,说明该系统具有丰富的混沌特性.首先对该忆阻混沌系统的基本动力学行为进行了理论分析和数值仿真,如平衡点稳定性、对称性,Lyapunov指数和维数,分岔图和Poincare截面等.同时,建立了模拟该忆阻混沌系统的SPICE(simulation program with integrated circuit emphasis)电路,给出了不同参数下的电路实验相图,其仿真结果与数值分析相符,从而验证了该忆阻混沌系统的混沌产生能力.由于脉冲同步只在离散时刻传递信息,能量消耗小,同步速度快,易于实现单信道传输,因而在混沌保密通信中更具有实用性.因此,本文从最大Lyapunov指数的角度实现了该忆阻混沌系统的脉冲混沌同步,数值仿真证实了忆阻混沌系统的存在性以及脉冲同步控制的可行性,为进一步研究该忆阻混沌系统在语音保密通信和信息处理中的应用提供了实验基础.     

Effect of metal oxide arrester on the chaotic oscillations in the voltage transformer with nonlinear core loss model using chaos theory

In this paper, controlling chaos when chaotic ferroresonant oscillations occur in a voltage transformer with nonlinear core loss model is performed. The effect of a parallel metal oxide surge arrester on the ferroresonance oscillations of voltage transformers is studied. The metal oxide arrester(MOA) is found to be effective in reducing ferroresonance chaotic oscillations. Also the multiple scales method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes sub-harmonic, quasi-periodic, and also chaotic oscillations. In this paper, the chaotic behavior and various ferroresonant oscillation modes of the voltage transformer is studied. This phenomenon consists of different types of bifurcations such as period doubling bifurcation(PDB), saddle node bifurcation(SNB), Hopf bifurcation(HB), and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are illustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via the multiple scales method to obtain Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system.     

基于有源广义忆阻的无感混沌电路研究

采用常见元器件等效实现一个广义忆阻器, 进而制作出一个电路特性可靠的非线性电路, 有助于忆阻混沌电路的非线性现象的实验展示及其所产生的混沌信号的实际工程应用. 基于忆阻二极管桥电路, 构建了一种无接地限制的、易物理实现的一阶有源广义忆阻模拟器; 由该模拟器并联电容后与RC桥式振荡器线性耦合, 实现了一种无电感元件的忆阻混沌电路; 建立了无感忆阻混沌电路的动力学模型, 开展了相应的耗散性、平衡点、稳定性和动力学行为等分析. 结果表明, 无感忆阻混沌电路在相空间中存在分布2个不稳定非零鞍焦的耗散区和包含1个不稳定原点鞍点的非耗散区; 当元件参数改变时, 无感忆阻混沌电路有着共存分岔模式和共存吸引子等非线性行为. 研制了实验电路, 该电路结构简单、易实际制作, 实验测量和数值仿真两者结果一致, 验证了理论分析的有效性.     

Hopf bifurcation and chaos in a single inertial neuron model with time delay

A delayed differential equation modelling a single neuron with inertial term subject to time delay is considered in this paper. Hopf bifurcation is studied by using the normal form theory of retarded functional differential equations. When adopting a nonmonotonic activation function, chaotic behavior is observed. Phase plots, waveform plots, and power spectra are presented to confirm the chaoticity.Received: 19 December 2003, Published online: 21 October 2004PACS: 05.45.-a Nonlinear dynamics and nonlinear dynamical systems     

A novel four-wing non-equilibrium chaotic system and its circuit implementation

In this paper, we construct a novel, 4D smooth autonomous system. Compared to the existing chaotic systems, the most attractive point is that this system does not display any equilibria, but can still exhibit four-wing chaotic attractors. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, bifurcation diagram, and Poincaré maps. There is little difference between this chaotic system without equilibria and other chaotic systems with equilibria shown by phase portraits and Lyapunov exponents. But the bifurcation diagram shows that the chaotic systems without equilibria do not have characteristics such as pitchfork bifurcation, Hopf bifurcation etc. which are common to the normal chaotic systems. The Poincaré maps show that this system is a four-wing chaotic system with more complicated dynamics. Moreover, the physical existence of the four-wing chaotic attractor without equilibria is verified by an electronic circuit.     

自调频混沌系统及其调频码耦合同步

提出了一个闭环自调频混沌系统, 对压控振荡器输出进行采样, 采样值经非线性变换后产生控制压控振荡器下一时刻频率的调频码. 利用一维分岔图、二维分岔图和Lyapunov指数等研究了该系统的动力学行为; 并利用峰值均值功率比、频谱以及输出信号的相关函数等分析了该系统的应用特性. 研究表明, 该系统有复杂的动力行为, 展现分岔、多稳态和混沌等现象, 产生的信号具有低峰值均值功率比和宽频带的特性. 同时还讨论了利用调频码实现系统同步的可能性, 证实了简单的控制器可以实现自调频系统的同步. 在电路实验中, 压控振荡器用数字频率合成技术实现, 实验结果与理论分析一致. 关键词： 混沌 多稳态 峰值均值功率比 同步     

A memristor oscillator based on a twin-T network

A novel inductance-free nonlinear oscillator circuit with a single bifurcation parameter is presented in this paper. This circuit is composed of a twin-T oscillator, a passive RC network, and a flux-controlled memristor. With an increase in the control parameter, the circuit exhibits complicated chaotic behaviors from double periodicity. The dynamic properties of the circuit are demonstrated by means of equilibrium stability, Lyapunov exponent spectra, and bifurcation diagrams. In order to confirm the occurrence of chaotic behavior in the circuit, an analog realization of the piecewise-linear flux-controlled memristor is proposed, and Pspice simulation is conducted on the resulting circuit.     

A four-wing and double-wing 3D chaotic system based on sign function

Many four-wing chaotic systems have been developed based on cross product or quadratic operations. Differently, we construct a three-dimensional chaotic system generating four-wing or double-wing attractors by virtue of sign function. Dynamical properties such as equilibrium points, Poincaré map, Lyapunov exponent spectra, Hopf bifurcations and bifurcation diagrams of the system are theoretically and numerically analyzed. Results of mathematical analyses and simulation tests indicate that the proposed chaotic system can keep chaotic to generate four-wing or double-wing attractors within a large scope of parameters. The system also shows hyperchaotic behaviors in some parameter range. Besides, circuit implementation of the chaotic system is studied. That proves the system is physically realizable.     

Generalized analytical solutions for certain coupled simple chaotic systems

We present a generalized analytical solution to the normalized state equations of a class of coupled simple secondorder non-autonomous circuit systems. The analytical solutions thus obtained are used to study the synchronization dynamics of two different types of circuit systems, differing only by their constituting nonlinear element. The synchronization dynamics of the coupled systems is studied through two-parameter bifurcation diagrams, phase portraits, and time-series plots obtained from the explicit analytical solutions. Experimental figures are presented to substantiate the analytical results. The generalization of the analytical solution for other types of coupled simple chaotic systems is discussed. The synchronization dynamics of the coupled chaotic systems studied through two-parameter bifurcation diagrams obtained from the explicit analytical solutions is reported for the first time.     

基于一阶广义忆阻器的文氏桥混沌振荡器研究

通过在文氏桥振荡器中引入广义忆阻器和LC吸收网络,提出了一种忆阻文氏桥混沌振荡器.建立了忆阻文氏桥混沌振荡器的动力学模型,研究了它的平衡点和稳定性,进一步开展了电路元件参数变化时的动力学行为分析.研究发现,忆阻文氏桥混沌振荡器有3个确定的平衡点,其稳定性取决于电路元件参数,当参数发生变化时,存在周期振荡、混沌振荡、快慢效应等复杂的非线性现象.实验电路简单易制作,实验波形和数值仿真一致,较好地验证了理论分析结果.     

忆阻混沌振荡器的动力学分析

忆阻器(memristor)是一种有记忆功能的非线性电阻器,它是除电阻器、电容器和电感器之外的第四种基本电路元件.采用一个具有光滑磁控特性曲线的忆阻器和一个负电导替换蔡氏振荡器中的蔡氏二极管,导出了一个基于忆阻器的振荡器电路.采用常规的动力学分析手段研究了电路参数和初始条件变化时该光滑忆阻振荡器的动力学特性.研究结果表明,光滑忆阻振荡器与一般的混沌系统完全不同,它的动力学行为除了与电路参数有关外,还极端依赖于电路的初始条件,存在瞬态混沌和状态转移等奇异的非线性物理现象.     

分段线性混沌电路的综合方法研究

本文研究了分段线性混沌电路的一种电路综合方法.首先根据电路系统的特征值参数,确定非线性元件参数和线性一端口电路的导纳.然后根据导纳函数确定与之对应的一端口电路形式.在电路综合过程中,本文采用两类基本导纳函数的并联形式实现一端口电路,可以始终使所用电感和电容为正值,所用负电阻共地,便于混沌电路的实现.最后给出了混沌系统电路综合的实例. 关键词： 混沌电路 综合 分段线性     

Design and implementation of a novel multi-scroll chaotic system

This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by constructing triangular wave, sawtooth wave and hysteresis sequence. The presented new multi-scroll chaotic system is different from the classical multi-scroll chaotic Chua system in dimensionless state equations, nonlinear functions and maximum Lyapunov exponents. In addition, the basic dynamical behaviours, including equilibrium points, eigenvalues, eigenvectors, eigenplanes, bifurcation diagrams and Lyapunov exponents, are further investigated. The success of the design is illustrated by both numerical simulations and circuit experiments.     

迟滞混沌神经元/网络的控制策略及应用研究

为了保持神经网络在优化计算求解过程中结构不被改变, 以迟滞混沌神经元和迟滞混沌神经网络为研究对象, 提出了一种基于滤波跟踪误差的控制策略来实现神经元/网络的稳定控制. 采用该控制策略, 在不改变非线性特性发生机理的情况下, 神经元/网络可实现函数优化计算问题的求解. 所设计的控制律包含两部分: 一部分是系统进入滤波跟踪误差面时的等效控制部分, 另一部分为确保系统快速进入滤波跟踪误差面的控制部分. 采用Lyapunov方法对神经元/网络的控制进行了稳定性证明. 根据待寻优函数直接求得神经元的控制律, 在该控制律的作用下, 神经元/网络可逐渐稳定到优化函数的极值点, 从而实现优化问题的求解, 仿真实验结果验证了该控制方法在优化计算中的可行性和有效性.     

改进型细胞神经网络实现的忆阻器混沌电路

在通用细胞神经网络单元的基础上,本文利用忆阻器本身的非线性实现了一种改进型细胞神经网络单元.通过连接4个改进的细胞神经网络单元导出了一种基于状态控制细胞神经网络的忆阻器混沌电路.为了验证该方法的正确性,采用通用的电子器件构建了一个忆阻器的模拟等效电路,并对提出的电路进行了实验分析.实验结果与数值仿真结果的一致性表明采用改进型的细胞神经网络可以有效地实现忆阻器混沌电路.     

Integrator-based circuit-independent chaotic oscillator structure

An integrator-based chaotic oscillator structure composed of three cascaded inverting, noninverting, and differential integrators is presented. The nonlinearity responsible for folding the trajectories is introduced by a single switching diode which is controlled by the output of the first integrator in the cascade. Chaotic behavior is verified on the functional level of the structure rendering it circuit-independent. A possible circuit realization is given and a canonical single-parameter-controlled ordinary differential equation capturing the qualitative dynamics of similar fourth-order integrator-based chaotic oscillators is proposed.     

A strange novel chaotic system with fully golden proportion equilibria and its mobile microcomputer-based RNG application

A strange novel three-dimensional quadratic continuous autonomous chaotic system with fully golden proportion equilibria is proposed. It has only seven terms, three quadratic nonlinearities and one parameter ‘a’. The system equations have four equilibrium points and very interestingly all the equilibrium points have fully golden proportion values. Besides, this chaotic system has hidden amplitude control properties. The dynamic analyses of the system are presented such as equilibrium points, dissipativity, Lyapunov exponents, bifurcation diagrams, phase portraits and hidden amplitude control properties. Later, electronic circuit of the system is simulated in software and implemented in real environment. Finally, microcomputer-based random number generator (RNG) application and its NIST-800-22 tests are executed as another real-time application.